Double copy—from optics to quantum gravity: tutorial

To Quantum Optics

The theory of quantum propagator and time–dependent integrals of motion in quantum optics is reviewed as well as the properties of Wigner function, Q– function, and coherent state representation. Propagators and wave functions of a free particle, harmonic oscillator, and the oscillator with varying frequency are studied using time–dependent linear in position and momentum integrals of motion. S...

Three Dimensional Loop Quantum Gravity: Particles and the Quantum Double

It is well known that the quantum double structure plays an important role in three dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three dimensional Riemannian loop quantum gravity (LQG) coupled to a finite number of massive spinless point particles. In LQG, physical states are usually constructed from the notio...

Application of Quantum Inequalities to Quantum Optics

We establish a connection between quantum inequalities, known from quantum field theory on curved spacetimes, and the degree of squeezing in quantum-optical experiments. We prove an inequality which binds the reduction of the electric-field fluctuations to their duration. The bigger the level of fluctuation-suppression the shorter its duration. As an example of an application of this inequality...

Related to Quantum Gravity

Classification of finite dimensional irreducible representations of nonstandard q-deformation U ′ q(son) of the universal enveloping algebra U(so(n,C)) of the Lie algebra so(n,C) (which does not coincide with the Drinfeld–Jimbo quantized universal enveloping algebra Uq(son)) is given for the case when q is not a root of unity. It is shown that such representations are exhausted by representatio...

Quantum Optics